Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Pure shear beam

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Shear angle θ at a middle point (–□– M=1 N⋅m, –○– M=10 N⋅m)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Spatial derivative of shear angle θ at a middle point (–□– M=1 N⋅m, –○– M=10 N⋅m)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Free falling flexible pendulum

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Vertical displacement at tip point using 6 ANCF finite elements (–□– method 1, –○– method 2, and –Δ– method 3)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Magnitude of the ry vector at tip point using method 2with 6 ANCF finite elements (–□– k=0, –○– k=103, –Δ– k=104)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Different curvature definitions at tip point using method 3 with 40 ANCF finite elements (–□– |rss|, –○– ∂θ/∂s)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Magnitude of the rss vector at the middle point using 40 ANCF finite elements (–□– method 1, –○– method 2, and –Δ– method 3)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Shear angle at middle point using 40 ANCF elements (–□– method 1, –○– method 2, and –Δ– method 3)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Energy balance obtained using method 2 with 6 ANCF finite elements (–□– kinetic energy, –○– elastic energy, –Δ– potential energy, and — total energy)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Energy balance obtained using method 3 with 6 ANCF finite elements (–□– kinetic energy, –○– elastic energy, –Δ– potential energy, and — total energy)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Derivative of θ with respect to the arc length at tip point using 40 bilinear CRBF elements (–□– method 1 and –Δ– method 3)

Date of download: 11/14/2017 Copyright © ASME. All rights reserved. From: Curvature Expressions for the Large Displacement Analysis of Planar Beam Motions J. Comput. Nonlinear Dynam. 2017;13(1):011013-011013-12. doi:10.1115/1.4037226 Figure Legend: Shear angle at tip point using 24 bilinear CRBF elements (–□– method 1 and –Δ– method 3)